Venkatesh Radhakrishnan

Learn More
We present NC approximation schemes for a number of graph problems when restricted to geometric graphs including unit disk graphs and graphs drawn in a civilized manner. Our approximation schemes exhibit the same time versus performance trade-off as the best known approximation schemes for planar graphs. We also define the concept of -precision unit disk(More)
We prove the #P-hardness of the counting problems associated with various satisfiability, graph, and combinatorial problems, when restricted to planar instances. These problems include 3Sat, 1-3Sat, 1-Ex3Sat, Minimum Vertex Cover, Minimum Dominating Set, Minimum Feedback Vertex Set, X3C, Partition Into Triangles, and Clique Cover. We also prove the(More)
We consider the problem of placing a speciied number (p) of facilities on the nodes of a network so as to minimize some measure of the distances between facilities. This type of problem models a number of problems arising in facility location, statistical clustering, pattern recognition, and also a processor allocation problem in multiprocessor systems. We(More)
We characterize the complexity of a number of basic optimization problems for unit disk graphs speciied hierarchically as in BOW83, LW87a, Le88, LW92]. Both PSPACE-hardness results and polynomial time approximations are presented for most of the problems considered. These problems include minimum vertex coloring, maximum independent set, minimum clique(More)
We present an architecture and prototype implementation for a generic provenance database middleware (GProM) that is based on the concept of query rewrites, which are applied to an algebraic graph representation of database operations. The system supports a wide range of provenance types and representations for queries, updates, transactions, and operations(More)
Provenance is essential for auditing, data debugging, understanding transformations, and many additional use cases. All these use cases would benefit from provenance for transactional updates. We present a provenance model for snapshot isolation transactions extending the semiring framework with version annotations and updates. Based on this model, we(More)
We study the efficient approximability of basic graph and logic problems in the literature when instances are specified hierarchically as in [35] or are specified by 1-dimensional finite narrow periodic specifications as in [58]. We show that, for most of the problems Π considered when specified using k-level-restricted hierarchical specifications or(More)